Banks borrow from overseas markets. The largest such market by a wide margin is the USA. Cheap US dollars make their way around the world, variously driving up currencies and driving down interest rates offered by banks.

Here in Australia, there's been a great deal of consternation that the "Big 4" banks no longer closely follow the movements in the cash rate set by the Reserve Bank (our central bank). This is because central bank funds have fallen to less than half of the cost of funding for our banks -- they mostly get their cash from the US and relend it Australians.

When the crisis first broke, Australian bank rates rose even while central bank rates fell. And that's because international finance became much more expensive.